In the closest packing of is N atoms . There are

Options

A. N' Tetrahedral voids and '2N' octahedral voids
B. 2N' Tetrahedral voids and 'N' octahedral voids
C. 2N' Tetrahedral voids and '2N' octahedral voids
D. N' Tetrahedral voids and 'N' octahedral voids

Answer

To solve the problem of determining the number of tetrahedral and octahedral voids in a closest packing arrangement of N atoms, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Closest Packing**:
In closest packing, atoms are arranged in a way that maximizes the number of atoms in a given volume. The two common types of closest packing are face-centered cubic (FCC) and hexagonal close packing (HCP).

**Hint**: Closest packing arrangements can be visualized as layers of spheres stacked in a specific manner.

2. **Identifying Tetrahedral Voids**:
In a closest packing arrangement, each atom can create tetrahedral voids. Each atom contributes to one tetrahedral void above it and one below it. Therefore, for N atoms, there will be a total of 2N tetrahedral voids.

**Hint**: Remember that each layer of spheres contributes to voids in the layers above and below.

3. **Identifying Octahedral Voids**:
Octahedral voids are formed by the arrangement of six atoms surrounding a central void. In a close-packed structure, for every N atoms, there is one octahedral void. Hence, the number of octahedral voids will be equal to N.

**Hint**: Visualize the arrangement of spheres; the octahedral voids are located at the center of the arrangement of six surrounding spheres.

4. **Summarizing the Results**:
From the analysis, we conclude that:
- The number of tetrahedral voids = 2N
- The number of octahedral voids = N

5. **Choosing the Correct Option**:
Based on the derived values, we can evaluate the given options:
- Option A: N tetrahedral voids and 2N octahedral voids (Incorrect)
- Option B: 2N tetrahedral voids and N octahedral voids (Correct)
- Option C: 2N tetrahedral voids and 2N octahedral voids (Incorrect)
- Option D: N tetrahedral voids and N octahedral voids (Incorrect)

Therefore, the correct answer is **Option B: 2N tetrahedral voids and N octahedral voids**.

### Final Answer:
**2N tetrahedral voids and N octahedral voids.**